What effect does the rim of a fisbee have on its flight?

The primary purpose of the rim on a frisbee is to create an airfoil with a deep curvature. When you throw a frisbee, the edge of it comes in contact with the air. As the air flows over the top of the frisbee, it speeds up and the pressure drops. This creates lift.

A frisbee without a a rim can still fly, but it won't fly as well as one with a rim. A completely flat disk will fly but the "angle of attack" becomes more of a factor as to how well it flies. A disk without a rim will be less stable in flight. You can try a simple experiment to see what role the rim plays in the flight of the frisbee. Try to fly a frisbee upside down, then compare your results to throwing a frisbee in the conventional way.